The present paper deals with real infinite-dimensional normed spaces;
some of the
main concepts here make sense, and have been treated in the literature,
in the general context of topological Hausdorff linear spaces over reals.
A subset of a normed space X is a body if it is
different from X itself and is the
closure of its non-empty interior. A covering of X by bodies is
called a tiling ofX
whenever any two different members of it have disjoint interiors. The
elements of such
a covering are called tiles. A tiling is bounded
(respectively convex) whenever each tile is bounded (respectively
convex).